Algorithms for Computing Triangular Decompositions of Polynomial Systems

Abstract

We propose new algorithms for computing triangular decompositions of polynomial systems incrementally. With respect to previous works, our improvements are based on a {\em weakened} notion of a polynomial GCD modulo a regular chain, which permits to greatly simplify and optimize the sub-algorithms. Extracting common work from similar expensive computations is also a key feature of our algorithms. In our experimental results the implementation of our new algorithms, realized with the {\RegularChains} library in {\Maple}, outperforms solvers with similar specifications by several orders of magnitude on sufficiently difficult problems.